Recurrences for the Bernoulli and Euler numbers.
Remarks on sum of products of -twisted Euler polynomials and numbers.
Rota-Baxter operators and Bernoulli polynomials
We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and Bernoulli polynomials. We show how Rota-Baxter operators equalities rewritten in terms of Bernoulli polynomials generate identities for the latter.
Secant tree calculus
A true Tree Calculus is being developed to make a joint study of the two statistics “eoc” (end of minimal chain) and “pom” (parent of maximum leaf) on the set of secant trees. Their joint distribution restricted to the set {eoc-pom ≤ 1} is shown to satisfy two partial difference equation systems, to be symmetric and to be expressed in the form of an explicit three-variable generating function.
Semi-invariants of binary forms and identities for Bernoulli, Euler and Hermite polynomials
Some computational formulas for -Nörlund numbers.
Some congruence property of modular forms.
Some identities for multiple Dedekind sums attached to Dirichlet characters
Some identities of Bernoulli numbers and polynomials associated with Bernstein polynomials.
Some identities of degenerate special polynomials
In this paper, by considering higher-order degenerate Bernoulli and Euler polynomials which were introduced by Carlitz, we investigate some properties of mixed-type of those polynomials. In particular, we give some identities of mixed-type degenerate special polynomials which are derived from the fermionic integrals on Zp and the bosonic integrals on Zp.
Some identities on the generalized -Bernoulli numbers and polynomials associated with -Volkenborn integrals.
Some identities on the -Genocchi polynomials of higher-order and -Stirling numbers by the fermionic -adic integral on .
Some modular results on the Euler and Bernoulli polynomials
Some relationships between the analogs of Euler numbers and polynomials.
Some results from the tables of irregularity index of a prime
Some symmetric identities involving a sequence of polynomials.
Some variations and consequences of the Kummer-Mirimanoff congruences
Special multi-poly-Bernoulli numbers.
Stanovení Bernoulliho čísel. Součet aritmetické posloupnosti bez užití diferenčních posloupností
Stickelberger subideals related to Kummer type congruences